|
| |
|
|
A096535
|
|
a(0) = a(1) = 1; a(n) = (a(n-1) + a(n-2)) mod n.
|
|
14
|
|
|
|
1, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 10, 3, 0, 3, 3, 6, 9, 15, 5, 0, 5, 5, 10, 15, 0, 15, 15, 2, 17, 19, 5, 24, 29, 19, 13, 32, 8, 2, 10, 12, 22, 34, 13, 3, 16, 19, 35, 6, 41, 47, 37, 32, 16, 48, 9, 1, 10, 11, 21, 32, 53, 23, 13, 36, 49, 19, 1, 20, 21, 41, 62, 31, 20, 51, 71, 46, 40, 8, 48, 56
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
COMMENTS
|
Suggested by Leroy Quet
Three conjectures: (1) All numbers appear infinitely often, i.e. for every number k >= 0 and every frequency f > 0 there is an index i such that a(i) = k is the f-th occurrence of k in the sequence.
(2) a(j) = a(j-1) + a(j-2) and a(j) = a(j-1) + a(j-2) - j occur approximately equally often, i.e. lim {n -> infinity} x_n / y_n = 1, where x_n is the number of j <= n such that a(j) = a(j-1) + a(j-2) and y_n is the number of j <= n such that a(j) = a(j-1) + a(j-2) - j (cf. A122276).
(3) There are sections a(g+1), ..., a(g+k) of arbitrary length k such that a(g+h) = a(g+h-1) + a(g+h-2) for h = 1,...,k, i.e. the sequence is non-decreasing in these sections (cf. A122277, A122278, A122279). - Klaus Brockhaus, Aug 29 2006
a(A197877(n)) = n and a(m) <> n for m < A197877(n); see first conjecture. [Reinhard Zumkeller, Oct 19 2011]
|
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..10000
|
|
|
MATHEMATICA
|
l = {1, 1}; For[i = 2, i <= 100, i++, len = Length[l]; l = Append[l, Mod[l[[len]] + l[[len - 1]], i]]]; l
f[s_] := f[s] = Append[s, Mod[s[[ -2]] + s[[ -1]], Length[s]]]; Nest[f, {1, 1}, 80] (* Robert G. Wilson v, Aug 29 2006 *)
RecurrenceTable[{a[0]==a[1]==1, a[n]==Mod[a[n-1]+a[n-2], n]}, a, {n, 90}] (* Harvey P. Dale, Apr 12 2013 *)
|
|
|
PROG
|
(Haskell)
a096535 n = a096535_list !! n
a096535_list = 1 : 1 : f 2 1 1 where
f n x x' = y : f (n+1) y x where y = mod (x + x') n
-- Reinhard Zumkeller, Oct 19 2011
|
|
|
CROSSREFS
|
Cf. A079777, A096534, A096274 (location of 0's), A132678.
Sequence in context: A039705 A082118 A079344 * A126047 A023049 A171034
Adjacent sequences: A096532 A096533 A096534 * A096536 A096537 A096538
|
|
|
KEYWORD
|
easy,nonn,nice
|
|
|
AUTHOR
|
Franklin T. Adams-Watters, Jun 23 2004
|
|
|
STATUS
|
approved
|
| |
|
|
